An inverted pendulum on a cart is 53 cm long. The cart suddenly moves by 2.4 mm. Use gravitational acceleration of 9.81 m/s2. (a) We know from the inverted pendulum analysis that using proportional feedback for the pendulum, the system response is oscillatory. If K = 114.3 cm/rad, obtain the response of the pendulum (i. e., et)), its amplitude, and the period of oscillation. (b) Obtain the response function., et), for the same pendulum if we use proportional-plus-integral feedback with K = 114.3 cm/radian and K2 = 668.1 cm/s-radian.

What is magnetic flux? explain faraday's law of induction.

You are traveling in a car going at a constant speed of 100km/h down a long, straight highway. you pass another car going in the same direction which is traveling at a constant speed of 80km/h. as measured from your car's reference frame this other car is traveling at −20km/h. what is the acceleration of your car as measured from the other car's reference frame? what is the acceleration of the other car as measured from your car's reference frame?

Samir watches a 100-minute movie on his spaceship. maria's spaceshipe flies in the same direction as samir's spaceship but she observes his move to last 125 minutes and his spaceship to be 40 m long. how long does samir observe his own spaceship to be? according to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does marias voyage take according to samir?